Foster has never revealed her handsome sons’ paternity and has reportedly said she won’t tell the boys until they turn 21.

“The kids look like him [Gibson] but blonder,” said one amateur genealogist.

If Gibson, a father of eight, donated his sperm to Foster, it would explain her fierce loyalty to the troubled star while the rest of Hollywood shunned him over his anti-Semitic remarks and abusive treatment of Oksana Grigorieva, the Russian girlfriend who bore his last child, Lucia, 3.

Foster and Gibson became friends in 1994 when they starred together in “Maverick.” The two have remained close and often play poker together. Foster’s elder son was born in 1998.

Foster cast Gibson as the lead in her 2011 movie “The Beaver” and stood by him through a grueling press tour. “He’s so incredibly loving and sensitive,” she recently said. “I knew the minute I met him that I would love him the rest of my life.”

The other prime paternity possibility is Randy Stone, the openly gay casting-director friend of Foster who died of heart disease in 2007.

Stone’s mother, the Rev. Beverly Bates, recently told Britain’s Daily Mail, “Randy told me that Jodie said she’ll tell the boys who their father is when they’re 21.” Bates believes Stone is their father, although he never confirmed it: “He told me he had to sign documents. It was a secret he took to his grave.”

The boys also have another mom, movie producer Cydney Bernard, whom Foster praised in her speech as “one of the deepest loves of my life.” The two broke up in 2008.